Let a,b,c be the sides of an right-angled triangle. Let a,b be the sides at the right angle. Then a^2+b^2=c^2.
There are 2 ways to calculate the area of the figure. Either (a+b)^2 or 2ab+c^2. This gives us .
(a+b)^2=2ab+c^2 a^2+2ab+b^2=c^2+2ab a^2+b^2=c^2
This completes the Proof.